The theory of algebraic stacks emerged in
the late sixties
and early seventies in Monographie the works
of
P. Deligne, D. Mumford, and Publication language:
M. Artin.
The language of algebraic stacks has been
used repeatedly since then,
mostly in connection with moduli problems:
the increasing
demand for an accurate description of moduli
"spaces" came from various areas
of mathematics and mathematical physics.
Unfortunately the basic results on algebraic
stacks were
scattered in the literature and sometimes
stated without proofs.
The aim of this book is to fill this reference
gap by providing mathematicians
with the first systematic account of the
general theory
of (quasiseparated) algebraic stacks over
an arbitrary base scheme.
It covers the basic definitions and constructions,
techniques for extending scheme-theoretic
notions to stacks,
Artin's representability theorems, but also
new topics such
as the "issu-etale" topology. (in
French)
Aug. 1999 225 pp.
3-540-65761-4 16,900.
Springer
A Course for Mathematicians
In 1996-97 the Institute for Advanced Study
(Princeton, NJ)
organized a special year-long program designed
to teach mathematicians
the basic physical ideas which underlie the
mathematical
applications. The purpose is eloquently stated
in a letter written
by Robert MacPherson:
"The goal is to create and convey an
understanding,
in terms congenial to mathematicians, of
some fundamen-tal notions of physics ...
[and to] develop the sort of intuition
common among physicists for those who are
used to thought processes stemming
from geometry and algebra.
These volumes are a written record of the
program.
They contain notes from several long and
many short courses covering various
aspects of quantum field theory and perturbative
string theory.
The courses were given by leading physicists
and the notes were written either by
the speakers or by mathematicians who participated
in the program.
The book also includes problems and solutions
worked out by
the editors and other leading participants.
Interspersed are mathematical texts with
background material
and commentary on some topics covered in
the lectures.
These two volumes present the first truly
comprehensive
introduction to this field aimed at a mathematics
audience.
They offer a unique opportunity for mathematicians
and mathematical physicists to learn about
the beautiful & difficult
subjects of quantum field theory and string
theory.
Contents
Volume 1, Part 1.: Classical Fields and Supersymmetry
* P. Deligne and J. W. Morgan Notes on
supersymmetry
(following Joseph Bernstein) * P. Deligne
Notes on spinors
* P. Deligne and D. S. Freed Classical
field theory
* P. Deligne and D. S. Freed Supersolutions
* P. Deligne and D. S. Freed Sign manifesto
Volume 1, Part 2.: Formal Aspects of QFT
* P. Deligne Note on quantization * D.
Kazhdan
Introduction to QFT * E. Witten Perturbative
quantum field
theory * E. Witten Index of Dirac operators
* L. Faddeev Elementary introduction to
quantum field theory
* D. Gross Renormalization groups * P.
Etingof Note on
dimensional regularization * E. Witten
Homework
Volume 2, Part 3.: Conformal Field Theory
and Strings
* K. Gawedzki Lectures on conformal field
theory
* E. DHoker Perturbative string theory
* P. Deligne Super space descriptions of
super gravity
* D. Gaitsgory Notes on 2d conformal field
theory and string theory
* A. Strominger Kaluza-Klein compactifications,
supersymmetry,
and Calabi-Yau spaces
Volume 2, Part 4.: Dynamical Aspects of QFT
* E. Witten Dynamics of Quantum Field Theory
* N. Sieberg N = 1 supersymmetric field
theories in 4 dimensions
1999 1,552 pp.
0-8218-1198-3
0-8218-2014-1@(Paper ed.)
A.M.S.
This edition,
updated by Arlene O'Sean and Antoinette Schleyer
of the American Mathematical Society,
brings Ms. Swanson's work up to date,
reflecting the more technical reality of
publishing today.
While it includes information for copy editors,
proofreaders,
and production staff to do a thorough,
traditional copyediting and proofreading
of a manuscript and proof copy,
it is increasingly more useful to authors,
who have become intricately involved with
the typesetting of their manuscripts.
Contents
* Especially for authors * How to mark mathematical
manuscripts
* Mathematics in print * Techniques of handling
manu script and proof
* Processing a publication in mathematics
* Publication style
* Trends * Appendixes * Glossary
1999 102 pp.
0-8218-1961-5 .
A.M.S.
Contents
* The Iwahori-Hecke algebra of the symmetric
group
* Cellular algebras * The modular representation
theory of \mathscr{H}
* The q-Schur algebra * The Jantzen sum formula
and the blocks of \mathscr H
* Branching rules, canonical bases and decomposition
matrices
* Appendix A. Finite dimensional algebras
over a field
* Appendix B. Decomposition matrices * Index
of notation
1999 200 pp.
0-8218-1926-7
A.M.S.
Since physicists introduced supersymmetry
in the mid 1970s,
there have been great advances in the understanding
of
supersymmetric quantum field theories and
string theories.
These advances have had important mathematical
consequences as well.
The lectures featured in this book treat
fundamemtal concepts necessary
for understanding the physics
behind these mathematical applications. Freed
approaches the topic
with the assumption that the basic notions
of supersymmetric field
theory are unfamiliar to most mathematicians.
He presents the material intending to impart
a firm grounding in the elementary ideas.
The first half of the book offers expository
introductions to superalgebras,
supermanifolds, classical field theory, free
quantum theories,
and super Poincar groups.
The second half covers specific models and
describes some
of their geometric features.
The overall aim is to explain the classical
supersymmetric field theories
that are basic for applications in quantum
mechanics and quantum field theory,
thereby providing readers with sufficient
background to explore the quantum ideas.
Contents
* What are fermions? * Lagrangians and symmetries
* Supersymmetry in various dimensions
* Theories with two supersymmetries
* Theories with more supersymmetry
1999 124 pp.
0-8218-1953-4
A.M.S.
We have been curious about numbers and prime
numbers
since antiquity. One notable new direction
this century
in the study of primes has been the influx
of ideas from probability.
The goal of this book is to provide insights
into the prime numbers
and to describe how a sequence so tautly
determined can incorporate
such a striking amount of randomness.
There are two ways in which the book is exceptional.
First, some familiar topics are covered with
refreshing insight and or from new points
of view.
Second, interesting recent developments and
ideas are presented
that shed new light on the prime numbers
& their distribution among the rest of
the integers.
This book is suitable for anyone who has
had a little number theory and some advanced
calculus involving estimates.
This book is the English translation from
the French edition.
1999 120 pp.
0-8218-1647-0
A.M.S.
The common thread throughout this book is
aperiodic tilings;
the best-known example is the kite and dart?
tiling.
This tiling has been widely discussed, particularly
since 1984 when
it was adopted to model quasicrystals. The
presentation uses many
different areas of mathematics and physics
to analyze the new
features of such tilings.
Although many people are aware of the existence
of aperiodic tilings,
and maybe even their origin in a
question in logic, not everyone is familiar
with their subtleties
and the underlying rich mathematical theory.
For the interested reader, this book fills
that gap.
Understanding this new type of tiling requires
an unusual variety of specialties,
including ergodic theory, functional analysis,
group theory and ring theory
from mathematics, and statistical mechanics
and wave diffraction from physics.
1999 128 pp.
0-8218-1933-X
A.M.S.
Continuous and Approximation Theories
Vol. 2: Abstract Hyperbolic-like Systems
over a Finite Time Horizon
This is the second volume of a comprehensive
and up-to-date two-volume treatment
of quadratic optimal control theory for partial
differential equations
over a finite or infinite time horizon, and
related differential (integral)
and algebraic Riccati equations.
Both continuous theory and numerical approximation
theory are included.
The authors use an abstract space, operator
theoretic approach,
which is based on semigroups methods, and
which unifies across
a few basic classes of evolution.
The various abstract frameworks are motivated
by, and ultimately
directed to partial differential equations
with boundary point control.
Dec. 1999 400pp
0-521-58401-9
Vol. 74: Lasiecka, I. / Lasiecka, R.:
Control Theory for Partial Differential Equations:
Continuous & Approximation Theories,
Vol. 1: Abstract Parabolic Systems
Dec. 1999 600 pp. 0-521-43408
Cambridge
Theory and Applications
In Semimodular Lattices: Theory and Applications
Manfred Stern
uses successive generalizations of distributive
and modular lattices to outline the development
of semimodular lattices
from Boolean algebras.
He focuses on the important theory of semimodularity,
its many ramifications, and its applications
in discrete mathematics, combinatorics, and
algebra.
The book surveys and analyzes Garrett Birkhof
concept of semimodularity
and the various related concepts in lattice
theory,
and it presents theoretical results as well
as
applications in discrete mathematics group
theory and universal algebra.
July 1999 384pp
0-521-46105-7
Cambridge
This book is treats optimal control problems
for systems described by
ordinary and partial differential equations,
using an approach that unifies finite dimensional
and infinite dimensional nonlinear programming.
Problems include control and state constraints
and target conditions.
Applications of the theory include nonlinear
systems described
by partial differential equations of hyperbolic
and parabolic type
and results on convergence of suboptimal
controls.
Altthough written at a level suuitable for
beginning graduate students
in applied mathematics this comprehensive
treatment will also be
a valuable reference for researchers in control
theory.
(Series Change / from Cambridge Studies in
Advancedmathematics)
July 1999 616 pp.
0-521-45125-6
Cambridge